Section 1
A
$G=S_{3}, H=\{\varepsilon, \beta, \delta\}$
$G=S_{3}, H=\{\varepsilon, \alpha\}$
$G=\mathbb{Z}_{15}, H=\langle 5\rangle$
$$G=D_{4}, H=\left\{R_{0}, R_{4}\right\}$$(For $D_{4}$, see page $\left.69 .\right)$
$$G=S_{4}, H=A_{a}$$(For $A_{A}$ see page 81$)$
ndicate the order and index of each of the subgroups in parts 1 to 5 .